Question

Guys can you please help me I’m stuck

Answer 1

The graph of the ellipse is shown in the attachment

vertices; ( -5,0) and (5,0)

co-vertices; (0, -2) and (0, 2)

foci; (
`√(21)`,0), (
`-√(21)`,0)

Explanation:

The vertices and co-vertices of the ellipse are on the graph. They represent the turning points of the ellipse.

To determine the foci of the ellipse we write the given equation in standard form by dividing both sides by 100 and then simplifying;

`(x^(2) )/(25)+(y^(2) )/(4)=1`

We then determine the distance c from the center to the focus;

`c^(2)=a^(2)-b^(2)`

`c=√(25-4)=√(21)`

The foci of the ellipse are thus; (
`√(21)`,0), (
`-√(21)`,0)